CANTON - Count on Cantor

no tags 

One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below.

1/1 1/2 1/3 1/4 1/5 ...
2/1 2/2 2/3 2/4
3/1 3/2 3/3
4/1 4/2
5/1

In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.

Input

The input starts with a line containing a single integer t <= 20, the number of test cases. t test cases follow.

Then, it contains a single number per line.

Output

You are to write a program that will read a list of numbers in the range from 1 to 10^7 and will print for each number the corresponding term in Cantor's enumeration as given below.

Example

Input:
3
3
14
7

Output:
TERM 3 IS 2/1
TERM 14 IS 2/4
TERM 7 IS 1/4

hide comments
epsilonalpha: 2016-06-24 18:56:10

AC in first try, 0.06 seconds in Java. Just observe the pattern and the rest is very simple, no algorithm needed!

rishabh_1997: 2016-06-19 13:08:28

A very nice question... Just pick a paper & try to find the pattern
You will enjoy when you will finally get AC :)

AC in 2nd go, just missed that "IS" in caps.

xinnix: 2016-06-17 19:37:26

Easy but nice question.

blueranger: 2016-06-16 16:32:33

Easy ... AC in one go.... 0.00 Time !!

top_gun007: 2016-06-14 11:16:09

easy one

gustavoaca1997: 2016-06-10 07:44:16

Yeah! AC in 1 go, but I was thinking by many hours hehe. Thanks to the comments I searched and learned something that I did not know (I think that in my next trimester I'm going to study it): Triangular Numbers. Very useful!

mkfeuhrer: 2016-06-03 22:53:39

observe a while......get something diagonally related to sum ... AC in 1 go :-)

gkr007: 2016-06-01 10:30:14

AC in 1 go :)!!

bhushangawde: 2016-05-16 08:10:43

easy AC in one go! :D My 20th !!

satoruu: 2016-04-23 00:21:21

Once you get the pattern, it will be easy. Think about math and geometry.

P.S: It was kinda funny, got WA on my first try because I was writing "is" instead of "IS", so watch out :)


Added by:Thanh-Vy Hua
Date:2005-02-27
Time limit:5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL 6 VB.net
Resource: ACM South Eastern European Region 2004